ln(x)+ln(x^2-8)=ln(8x)

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Solution for ln(x)+ln(x^2-8)=ln(8x) equation: 


Simplifying
ln(x) + ln(x2 + -8) = ln(8x)

Multiply ln * x
lnx + ln(x2 + -8) = ln(8x)

Reorder the terms:
lnx + ln(-8 + x2) = ln(8x)
lnx + (-8 * ln + x2 * ln) = ln(8x)
lnx + (-8ln + lnx2) = ln(8x)

Reorder the terms:
-8ln + lnx + lnx2 = ln(8x)

Remove parenthesis around (8x)
-8ln + lnx + lnx2 = ln * 8x

Reorder the terms for easier multiplication:
-8ln + lnx + lnx2 = 8ln * x

Multiply ln * x
-8ln + lnx + lnx2 = 8lnx

Solving
-8ln + lnx + lnx2 = 8lnx

Solving for variable 'l'.

Move all terms containing l to the left, all other terms to the right.

Add '-8lnx' to each side of the equation.
-8ln + lnx + -8lnx + lnx2 = 8lnx + -8lnx

Combine like terms: lnx + -8lnx = -7lnx
-8ln + -7lnx + lnx2 = 8lnx + -8lnx

Combine like terms: 8lnx + -8lnx = 0
-8ln + -7lnx + lnx2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-8 + -7x + x2) = 0

Factor a trinomial.
ln((-1 + -1x)(8 + -1x)) = 0


Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve:

Simplifying
ln = 0

Solving
ln = 0

Move all terms containing l to the left, all other terms to the right.

Simplifying
ln = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(-1 + -1x)' equal to zero and attempt to solve:

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

Move all terms containing l to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + -1x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1x = 0 + 1
-1x = 0 + 1

Combine like terms: 0 + 1 = 1
-1x = 1

Add 'x' to each side of the equation.
-1x + x = 1 + x

Combine like terms: -1x + x = 0
0 = 1 + x

Simplifying
0 = 1 + x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 3
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

Move all terms containing l to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Add 'x' to each side of the equation.
-1x + x = -8 + x

Combine like terms: -1x + x = 0
0 = -8 + x

Simplifying
0 = -8 + x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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